For a short sentence of this sort, you don't need the comma. But it's not wrong, and if you have a long sentence with extended clauses, it can help the rhythm. Also, it can sometime help disambiguate, which can happen particularly in negative constructions. Consider "He didn't go to the doctor because he was sick." Maybe he went because he knew the doctor socially. Or maybe he had to cancel a routine appointment because he wasn't feeling well enough to leave the house. A comma would make it clear that something of the second sort happened.

No. You don't use a comma with 'because'. He went to the doctor because he was ill.